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A MULTISCALE SYSTEMS BIOLOGY APPROACH FOR COMPUTER SIMULATION-BASED
PREDICTION OF BONE REMODELING
M.I. Pastrama†, S. Scheiner†, P. Pivonka‡, C. Hellmich†
† Institute for Mechanics of Materials and Structures, Vienna University of Technology, Austria; ‡ Australian Institute for Musculoskeletal Science, The University of Melbourne, Australia
E-mail: maria-ioana.pastrama@tuwien.ac.at
9. Jahrestagung der Deutschen Gesellschaft für Biomechanik, 6. – 8. Mai 2015, Bonn, Deutschland
Introduction
Materials and Methods
Results & Discussion
Length scales in bone Mathematical model
𝑓𝑣𝑎𝑠 =𝑉𝑣𝑎𝑠
𝑉𝑅𝑉𝐸𝑎𝑛𝑑
𝑑𝑓𝑣𝑎𝑠
𝑑𝑡= 𝑓𝑣𝑎𝑠(𝐶𝑂𝐶𝐴
𝑣𝑎𝑠𝑘𝑟𝑒𝑠𝑣𝑎𝑠 − 𝐶𝑂𝐵𝐴
𝑣𝑎𝑠 𝑘𝑓𝑜𝑟𝑚𝑣𝑎𝑠 )
Bone remodeling, a remarkable process taking place throughout the whole life of vertebrates,
is driven by the cellular activity of bone-resorbing osteoclasts, bone-forming osteoblasts, and
load-sensing osteocytes, and governed by biochemical factors, such as the
RANKL/RANK/OPG pathway, parathyroid hormone (PTH), and transforming growth factor
beta (TGF-β) [1]. Here a mathematical model derived from a previously published modeling
strategy [2, 3] is presented, based on which the dynamics of bone remodeling can be accurately
predicted. We consider the different length scales found in bone by means of a multiscale
systems biology approach, and follow the evolutions of osteoclast and osteoblast
concentrations due to biochemical factors and changes in the mechanical loading. Thereby, the
effects of porosity changes are explicitly taken into account. Mechanical regulation of the
process is considered by coupling the mathematical systems biology-based model with an
experimental, multiply validated continuum micromechanics representation of bone [4], and
a recently developed multiscale poromechanics model [5], based on which the length scale-
specific strain states in the vicinity of the bone remodeling-driving cells can be estimated. The
model is applied for studying the development of the bone composition in the course of
mechanical dis- and overuse, as well as of postmenopausal osteoporosis (PMO).
References
TGFb
RANKRANKL
OPG
PTH
PROLIF-
ERATION
osteoblast
progenitor cells
osteoblast
precursor cells
active
osteo-
blasts
osteoclast precursor cells
active osteoclasts
strainsextravascular
bone matrix
DIFFE
RENTIATION
DIF
FEREN
TIA
TION
DIFFEREN
TIA
TIO
N
APOPTOSIS
APOPTOSIS
RANK-R
ANKL
BIN
DIN
G
PROLIFERA
TION
STIMULAT
ION
5 cm 1 cm
L
longitudinal section cross section
l d
extravascular
bone matrix
vascular pore
spacemechanical loading
vascular pore space
I
II
III
I: images of long bone at the macroscopic scale [6]
II: representative volume element (RVE) of cortical
bone microstructure (L >> l >> d [7])
III: main mechanisms involved in bone remodeling
Model assumptions
• Bone remodeling is considered to take place in the
vascular pore space, where ”teams” of
osteoblasts and osteoclasts work together
• Cell populations are considered in terms of molar
vascular concentrations 𝑪𝒊𝒗𝒂𝒔 [8]
• Biochemical regulation is mainly realized via the
RANKL/RANK/OPG pathway and TGF-β; the
concentrations of these factors are also considered
at the level of vascular pores,𝑪𝒋𝒗𝒂𝒔
• Mechanical regulation is evaluated by means of the
strain energy density (SED) of the extravascular
matrix Ψ𝑒𝑥𝑣𝑎𝑠; increased mechanical loading leads to
increased osteoblast precursor proliferation [9]
decreased RANKL-production, downregulation
of RANKL-RANK binding and, thus,
downregulation of osteoclast differentiation [10]
Evolutions of the vascular cell concentrations of osteoblast progenitors (OCP),
active osteoblasts (OBA) and active osteoclasts (OCA):
𝑑𝐶𝑂𝐵𝑃𝑣𝑎𝑠
𝑑𝑡= 𝒟𝑂𝐵𝑈(𝑇𝐺𝐹𝛽)𝐶𝑂𝐵𝑈
𝑣𝑎𝑠 +[𝒫𝑂𝐵𝑃(𝛹𝑒𝑥𝑣𝑎𝑠) − 𝒟𝑂𝐵𝑃(𝑇𝐺𝐹𝛽)]𝐶𝑂𝐵𝑃𝑣𝑎𝑠−
𝐶𝑂𝐵𝑃𝑣𝑎𝑠
𝑓𝑣𝑎𝑠
𝑑𝑓𝑣𝑎𝑠𝑑𝑡
𝑑𝐶𝑂𝐵𝐴𝑣𝑎𝑠
𝑑𝑡= 𝒟𝑂𝐵𝑃(𝑇𝐺𝐹𝛽)𝐶𝑂𝐵𝑃
𝑣𝑎𝑠 −𝒜𝑂𝐵𝐴𝐶𝑂𝐵𝐴𝑣𝑎𝑠 −
𝐶𝑂𝐵𝐴𝑣𝑎𝑠
𝑓𝑣𝑎𝑠
𝑑𝑓𝑣𝑎𝑠𝑑𝑡
𝑑𝐶𝑂𝐶𝐴𝑣𝑎𝑠
𝑑𝑡= 𝒟𝑂𝐶𝑃( 𝑅𝐴𝑁𝐾𝐿 ∙ 𝑅𝐴𝑁𝐾 ,𝛹𝑒𝑥𝑣𝑎𝑠)𝐶𝑂𝐶𝑃
𝑣𝑎𝑠−𝒜𝑂𝐶𝐴(𝑇𝐺𝐹𝛽)𝐶𝑂𝐶𝐴𝑣𝑎𝑠 −
𝐶𝑂𝐶𝐴𝑣𝑎𝑠
𝑓𝑣𝑎𝑠
𝑑𝑓𝑣𝑎𝑠𝑑𝑡
Concentration changes due to
biochemical factors
Concentration changes due to
geometry
Definition and evolution of the vascular porosity:
𝛹𝑒𝑥𝑣𝑎𝑠 =𝛹𝑚𝑎𝑐𝑟𝑜 −𝛹𝑣𝑎𝑠𝑓𝑣𝑎𝑠
1 − 𝑓𝑣𝑎𝑠
Definition of the extravascular strain energy density:
OBU…uncommitted osteoblast
progenitors
𝒟…differentiation rate
𝒜…apoptosis rate
𝒫…proliferation rate
𝑉𝑣𝑎𝑠…volume of vascular pores
𝑉𝑅𝑉𝐸…volume of RVE
𝑘𝑟𝑒𝑠𝑣𝑎𝑠…bone resorption coefficient
𝑘𝑓𝑜𝑟𝑚𝑣𝑎𝑠 …bone formation coefficientΨ𝑚𝑎𝑐𝑟𝑜, Ψ𝑣𝑎𝑠…macroscopic and vascular SED, respectively,
resulting from the multiscale poromechanics model
[1] S. Theoleyre et al. (2004). Cytokine Growth F R, 15(6): 457–75.
[2] S. Scheiner et al. (2013). Comput Methods Appl Mech Eng, 254: 181-196.
[3] S. Scheiner et al. (2014). Int J Numer Meth Bio. 30(1):1–27.
[4] C. Hellmich et al. (2008). Ann Biomed Engrg, 36(1): 108–122.
[5] S. Scheiner et al. (2015). Submitted to Biomech Model Mechanobiol.
[6] S. Weiner and H.D Wagner (1998). Annu Rev Mater Sci, 28: 271-298.
[7] A. Zaoui (2002). J Eng Mech-ASCE, 128: 808-816.
[8] V. Lemaire et al. (2004). J Theor Biol, 229: 293-309.
[9] D. Kaspar et al. (2002). J Biomech, 35(7): 873-880.
[10] C. Liu et al. (2010). Bone, 46(5): 1449-1456.
[11] L. Vico and and C. Alexandre. J Bone Min Res, 7(S2): 445–447.
[12] S. Manolagas (2000). Endocr Rev, 21: 115-137.
[13] A. Tomkinson et al. (1998). J Bone Miner Res, 13: p1243-1250.
[14] N. Bonnet and S. Ferrari. IBMS BoneKey, 7: 235-248.
[15] R. Nikander (2010). Osteoporosis Int, 21:1687–1694.
Simulation of postmenopausal osteoporosis
• PMO is modeled biochemically, by introducing [12,13]:
a disease-related increase of the vascular concentration of
RANKL (leading to increased osteoclast concentration and
bone resorption)
a reduction of the mechanoresponsiveness
• The simulated decrease of the bone matrix volume fraction
with PMO agrees well with corresponding clinical data [14]
Simulation of bone disuse (microgravity)
• Mechanical loading is prescribed in
terms of the stress tensor of cortical
bone:
• The increase in vascular porosity due to
disuse reaches a plateau with a constant
value 𝑓𝑣𝑎𝑠 = 0.21 after approximately
1200 days (Fig. 1), when the cells return
to their initial concentrations
𝐶𝑖𝑣𝑎𝑠 𝐶𝑖,𝑖𝑛𝑖
𝑣𝑎𝑠 = 1 (Fig. 2)
• The simulation is in agreement with
experiments on astronauts during and
after space flight [11]
• The return of 𝑓𝑣𝑎𝑠 to its initial value
after disuse is much more rapid when
simulated with the vascular scale-related
model, compared to previous,
macroscopic formulations [2, 3]
normal:
disuse:
S33 = -30 MPa
S33 = -25 MPaΣ𝑐𝑜𝑟𝑡 =
0 0 00 0 00 0 Σ33
Simulation of bone overuse
• Overuse is simulated by setting S33 = -35 MPa
• Compared to previous, macroscopic model formulations, the
overuse does not lead to a rapid increase and negative values of
the vascular porosity; instead, the increase of 𝑓𝑣𝑎𝑠 over time is
slow and never reaches negative values (as shown in the figure)
• The simulation agrees qualitatively with experiments associating
long-term sport-specific exercise loading with thicker cortex at
certain areas [15]Figure 2: Evolution of bone cell concentrations
for 2000 days of disuse
Figure 1: Evolution of the vascular porosity for
2000 days of disuse (𝑓𝑣𝑎𝑠,𝑖𝑛𝑖 = 0.05)
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